Costs, Benefits and the Internal Rate of Return toFirm Provided Training

Rita Almeida∗

The World Bank

Pedro CarneiroUniversity College London, Institute for Fiscal Studiesand Center for Microdata Methods and Practice

April 2006

Abstract

In this paper we estimate the rate of return to firm investments in human capital inthe form of formal job training. We use a panel of large firms with detailed informationon the duration of training, the direct costs of training, and several firm characteristics.Our estimates of the return to training vary substantially across firms. On average itis −7% for firms not providing training and 24% for those providing training. Resultssuggest that formal job training is a good investment for many firms and the econ-omy, possibly yielding higher returns than either investments in physical capital orinvestments in schooling. In spite of this, observed amounts of formal training are verysmall.

Keywords: On-the-Job Training, Panel Data, Production Function, Rate of Re-turnJEL classification codes: C23, D24, J31

∗We thank conference participants at the European Association of Labor Economists (Lisbon, 2004),Meeting of the European Economic Association (Madrid, 2004), the IZA/SOLE Meetings (Munich, 2004),ZEW Conference on Education and Training (Mannheim, 2005), the 2005 Econometric Society WorldCongress, and the 2006 Bank of Portugal Conference on Portuguese Economic Development. We thankespecially the comments made by Manuel Arellano, Ana Rute Cardoso, Pedro Telhado Pereira and StevePischke. Corresponding author: p.carneiro@ucl.ac.uk. Department of Economics, University College Lon-don, Room 228, Drayton House, London, UK. Phone: 020-7679 5824.

1. Introduction

Individuals invest in human capital over the whole life-cycle, and more than one half of life-

time human capital is accumulated through post-school investments on the firm (Heckman,

Lochner and Taber, 1998). This happens either through learning by doing or through formal

on-the-job training. In a modern economy, a firm cannot afford to neglect investments in the

human capital of its workers. In spite of its importance, economists know surprisingly less

about the incentives and returns to firms of investing in training compared with what they

know about the individual’s returns of investing in schooling.1 Similarly, the study of firm

investments in physical capital is much more developed than the study of firm investments

in human capital, even though the latter may be at least as important as the former in mod-

ern economies. In this paper we estimate the internal rate of return of firm investments in

human capital. We use a census of large manufacturing firms in Portugal, observed between

1995 and 1999, with detailed information on investments in training, its costs, and several

firm characteristics.2

Most of the empirical work to date has focused on the return to training for workers

using data on wages (e.g., Bartel, 1995, Arulampalam, Booth and Elias, 1997, Mincer, 1989,

Frazis and Loewenstein, 2005). Even though this exercise is very useful, it has important

drawbacks (e.g., Pischke, 2005). For example, with imperfect labor markets wages do not

fully reflect the marginal product of labor, and therefore the wage return to training tells us

1An important part of the lifelong learning strategies are the public training programs. There is muchmore evidence about the effectiveness (or lack of it) of such programs compared with the available evidenceon the effectiveness of the private on-the-job training.

2We will consider only formal training programs and abstract from the fact that formal and informaltraining could be very correlated. This is a weakness of most of the literature, since informal training is veryhard to measure.

3

little about the effect of training on productivity. Moreover, the effect of training on wages

depends on whether training is firm specific or general (e.g., Becker, 1962, Leuven, 2004).3

More importantly, the literature estimating the effects of training on productivity have little

or no mention of the costs of training (e.g. Bartel, 1991, 1994, 2000, Black and Lynch, 1998,

Barret and O’Connell, 1999, Dearden, Reed and Van Reenen, 2005). This happens most

probably due to lack of adequate data. As a result, we cannot interpret the estimates in

these papers as well defined rates of return.4

The data we use is unusually rich for this exercise since it contains information on the

duration of training, direct costs of training to the firm as well as productivity data. This

allow us to estimate both a production and a cost function and to obtain estimates of the

marginal benefits and costs of training to the firm. In order to estimate the total marginal

costs of training, we need information on the direct cost of training and on the foregone

productivity cost of training. The first is observed in our data while the second is the

marginal product of worker’s time while training, which can be estimated.

The major challenge in this exercise are the possible omitted variables and the endogenous

choice of inputs in the production and cost functions. Given the panel structure of our

data, we address these issues using the estimation methods proposed in Blundell and Bond

(2000). In particular, we estimate the cost and production functions using a first difference

instrumental variable approach, implemented with a GMM estimator. By computing first

differences we control for firm unobservable and time invariant characteristics. By using

3For example, Leuven and Oosterbek (2002, 2004) argue that they may be finding low or no effects oftraining because they are using individual wages as opposed to firm productivity.

4This shortcoming of the literature as been emphasized in Mincer (1989) and Machin and Vignoles (2001),among others.

4

lagged values of inputs to instrument current differences in inputs (together with lagged

differences in inputs to instrument current levels) we account for any correlation between

input choices and transitory productivity or cost shocks. Our instruments are valid as long

as input decisions in period t − 1 are made without knowledge of the transitory shocks in

the production and cost functions in period t.5

Several interesting facts emerge from our empirical analysis. First, in line with the pre-

vious literature (e.g., Pischke, 2005, Bassanini, Booth, De Paola and Leuven, 2005, Frazer

and Lowenstein, 2005) our estimates of the effects of training on productivity are high: an

increase in training per employee of 10 hours per year, leads to an increase in current produc-

tivity of 0.6%. Increases in future productivity are dampened by the rate of depreciation of

human capital but are still substantial. This estimate is below other estimates of the benefits

of training in the literature (e.g., Dearden, Reed and Van Reenen, 2005, Blundell, Dearden

and Meghir, 1999). If the marginal productivity of labor were constant (linear technology),

an increase in the amount of training per employee by 10 hours would translate into foregone

productivity costs of at most 0.5% of output (assuming all training occurred during working

hours).6 With decreasing marginal product of labor (and because roughly 50% of training

occurs outside normal working time) foregone productivity is much lower. Given this wedge

between the benefits and the foregone output costs of training, ignoring the direct costs of

training yields a rate of return to training that is absurdly high.

5This assumption is valid as long as there does not exist strong serial correlation in the transitory schocksin the data. Given the relatively short length of our panel our ability to test this assumption is limited.However, in the only other paper we know that applies these methods for studying the impact of trainingon productivity (with data for the UK aggregated by industry), using a long panel Dearden, Reed and VanReenen (2005) cannot reject that second order serial correlation in the first differences of productivity shocksis equal to zero. In their original application, Blundell and Bond (2000) also do not find evidence of secondorder serial correlation using firm level data for the UK.

6For an individual working 2000 hours a year, 10 hours corresponds to 0.5% of annual working hours.

5

Second, we estimate that, on average, foregone productivity accounts for less than 25% of

the total costs of training. This finding shows that the simple returns to schooling intuition

is inadequate for studying the returns to training, since it assumes negligble direct costs

of human capital accumulation. In particular, the coefficient on training in a production

function is unlikely to be a good estimate of the return to training.7 Moreover, without

information on direct costs of training, estimates of the return to training will be too high

since direct costs account for the majority of training costs (see also the calculations in Frazer

and Lowenstein, 2005).

Finally, our estimates of the internal rate of return to training vary across firms8. While

investments in human capital have on average negative return for those firms which do

not provide training, returns for firms providing training are quite high (24%). Such high

returns suggest that on-the-job training is a good investment for firms and for the economy

as a whole, possibly yielding higher returns than either investments in physical capital or

investments in schooling.

As a consequence, it is puzzling why these firm train on average such a small propor-

tion of the total hours of work (less than 1%). We conjecture that this could happen for

different reasons but unfortunately we cannot verify empirically the importance of each of

these hypotheses. First, it may be the result of a coordination problem (Pischke, 2005).

Given that the benefits of training need to be shared between firms and workers, each party

individually only sees part of the total benefit of training.9 Unless investment decisions are

7This is also likely to be a problem in wage regressions.8This is not surprising given that our parameter of interest is the internal rate of return to marginal

investments in training, and both the production and cost functions are nonlinear.9This may be also due to the so called ”poaching externality” (Stevens, 1994). See also Acemoglu and

Pischke (1998, 1999) for an analysis of the consequences of imperfect labor markets for firm provision of

6

coordinated and decided jointly, inefficient levels of investment may arise. Second, firms can

be constrained (e.g., credit constrained) and decide a suboptimal investment. Third, uncer-

tainty in the returns of this investment may lead firms to invest small amounts even though

the ex post average return is high.10 Consistent with this argument, we find an enormous

dispersion in the ex post returns to training (e.g., in our base specification the 5th percentile

of the distribution of internal rates of return is -16% and the 95% percentile is 66%). How-

ever, it is unlikely that uncertainty alone can justify such high rates of return. In our model

uncertainty only comes from future productivity shocks, since current costs and productivity

shocks are assumed to be known at the time of the training decision. The R-Squared of our

production functions (after accounting for firm fixed effects) is about 85%, suggesting that

temporary productivity shocks explain 15% of the variation in output. Since productivity

shocks are correlated over time this is an overestimate for the uncertainty faced by firms.

The paper proceeds as follows. Section 2 describes the data we use. In section 3, we

present our basic framework for estimating the production function and the cost function. In

section 4 we present our empirical estimates of the costs and benefits of training and compute

the marginal internal rate of return for investments in training. Section 5 concludes.

2. Data

We use the census of large firms (firms more than 100 employees) operating in Portugal

(Balanco Social). The information is collected with a mandatory annual survey conducted

general training.10Although what really matters for determining the risk premium is not uncertainty per se, but its corre-

lation with the rest of the market.

7

by the Portuguese Ministry of Employ. The data has information on hours of training

provided by the employers and on the direct training costs at the firm level. Other variables

available at the firm level include the firm’s location, ISIC 5-digit sector of activity, value

added, number of workers and a measure of the capital, given by the book value of capital

depreciation, average age of the workforce and share of males in the workforce. It also

collects several measures of the firm’s employment practices such as the number of hires and

fires within a year (which will be important to determine average worker turnover within

the firm). We use information for manufacturing firms between 1995-1999. This gives us

a panel of 1, 500 firms (corresponding to 5, 501 firm-year observations). On average, 53%

of the firms in the sample provide some training. All the variables used in the analysis are

defined in the annex.

Relative to other datasets that are used in the literature, the one we use has several

advantages for computing the internal rates of return of investments in training. First, in-

formation is reported by the employer. This may be better than having employee reported

information about past training if the employee recalls less and more imprecisely the infor-

mation about on-the-job training. Second, training is reported for all employees in the firm,

not just new hires. Third, the survey is mandatory for firms with more than 100 employees

(34% of the total workforce in 1995). This is an advantage since a lot of the empirical work

in the literature uses small sample sizes and the response rates on employer surveys tend to

be low.11 Fourth, it collects longitudinal information for training hours, firm productivity

11Bartel (1991) uses a survey conducted by the Columbia Business School with a 6% response rate. Blackand Lynch (1997) use data on the Educational Quality of the Worforce National Employers survey, which isa telephone conducted survey with a 64% ”complete” response rate. Barrett and O’Connell (2001) expandan EU survey and obtain a 33% response rate.

8

and direct training costs at the firm level. More than 50% of the firms are observed at least

twice during the period 1995-1999.12

Table 1 reports the descriptive statistics for the relevant variables in the analysis. We

divide the sample according to whether the firm provides any formal training and, if it does,

whether the training hours per employee are above the median (6.4 hours) for the firms

that provide training. We report medians rather than means to avoid extreme sensitivity to

extreme values. Firms that offer training programs and are defined as high training intensity

firms have a higher value added per employee and are larger than low training firms and firms

that do not offer training. Total hours on the job per employee (either working or training)

do not differ significantly across types of firms. High training firms also have a higher stock

of physical capital. The workforce in firms that provide training is more educated and is

older than the workforce in firms that do not offer training. The proportion of workers with

bachelor or college degrees is 6% and 3% in high and low training firms, versus 1.3% in non-

training firms. The workforce in firms that offer training has a higher proportion of male

workers.13 These firms also tend to have a higher proportion of more skilled occupations

such as higher managers and middle managers, as well as a lower proportion of apprentices.

High and low training firms differ significantly in their training intensity. Firms with a

small amount of training (defined as being below the median) offer 1.6 hours of training per

employee per year while those that offer a large amount of training offer 19 hours of training.

Even though the difference between the two groups of firms is large, the number of training

12Firms can leave the sample because they exit the market or because total employment is reduced to lessthan 100 employees.13Arulampalam, Booth and Bryan (2004) also find evidence for European countries that training incidence

is higher among men, and is positively associated with high educational attainment and a high position inthe wage distribution.

9

hours even for high training firms looks very small when compared with the 2055 average

annual hours on-the-job for the (0.9% of total time on-the-job). High training firms spend

9 times more in training per employee than low training firms. These costs are 0.01% and

0.3% of value added respectively. This proportion is rather small, but is in line with the

small amounts of training being provided.

In sum, firms train a rather small amount of hours. This pattern is similar to other

countries in Southern Europe (Italy, Greece, Spain) as well as in Eastern Europe (e.g.,

Bassanini, Booth, De Paola and Leuven, 2005). We find a lot of heterogeneity between firms

offering training, with low and high training firms being very different. Finally, the direct

costs of formal training programs are small (as a proportion of the firm’s value added) which

is in line with training a small proportion of the working hours.

3. Basic Framework

Our parameter of interest is the internal rate of return to the firm of an additional hour

of training per employee. This is the relevant parameter for evaluating the rationale for

additional investments in training, since firms compare the returns to alternative investments

at the margin. Let MBt+s be the marginal benefit of an additional unit of training in t and

MCt be the marginal cost of the investment in training at t. Assuming that the cost is

all incurred in one period and that the investment generates benefits in the subsequent N

periods, the internal rate of return of the investment is given by the rate r that equalizes

10

the present discounted value of net marginal benefits to zero:

N

s=1

MBt+s(1 + r)s

−MCTt = 0 (3.1)

Training involves a direct cost and a foregone productivity cost. Let the marginal training

cost be given by: MCTt = MCt + MFPt, where MCt is the marginal direct cost and

MFPt is the marginal product of foregone worker time. In the next sections we lay out the

basic framework which we use to estimate the components of MCTt and MBt+s. To obtain

estimates for MFPt and MBt+s, in section 3.1 we estimate a production function and to

obtain estimates for MCt in section 3.2 we will estimate a cost function.

3.1. Estimating the Production Function

We assume, as in so much of the literature, that the firm’s production function is semi-log

linear and that the firm’s stock of human capital determines the current level of output:

Yjt = AtKαjtL

βjt exp(γhjt + θZjt + µj + εjt) (3.2)

where Yjt is a measure of output in firm j and period t, Kjt is a measure of capital stock, Ljt is

the total number of employees in the firm, hjt is a measure of the stock of human capital per

employee in the firm and Zjt is a vector of firm and workforce characteristics. Given that the

production function is assumed to be identical for all the firms in the sample, µj captures

time-invariant firm heterogeneity and εjt captures time-varying firm specific productivity

shocks.

The estimation of production functions is a difficult exercise because inputs are chosen

11

endogenously by the firm and because many inputs are unobserved. Even though the inclu-

sion of firm time invariant effects may mitigate these problems (e.g., Griliches and Mairesse,

1995), this will not suffice if, for example, transitory productivity shocks determine the de-

cision of providing training (and the choice of other inputs). Recently, several methods have

been proposed for the estimation of production functions, such as Olley and Pakes (1996),

Levinsohn and Petrin (2000), Ackerberg, Caves and Frazer (2005) and Blundell and Bond

(2000).

We apply the methods for estimation of production functions proposed in Blundell and

Bond (2000), which build on Arellano and Bond (1991) and Arellano and Bover (1995). In

particular, we estimate the cost and production functions using (essentially) a first difference

instrumental variable approach, implemented with a GMM estimator. By computing first

differences we control for firm unobservable and time invariant characteristics (much of the

literature generally stops here). By using lagged values of inputs to instrument current

differences in inputs (together with lagged differences in inputs to instrument current levels)

we account for any correlation between input choices and transitory productivity or cost

shocks. Our instruments are valid as long as the transitory shocks in the production and

cost functions do not exhibit serial correlation of order equal or higher than two. Another

advantage of this approach is that it also corrects for biases generated by measurement error

in inputs.

As argued in Bond and Soderbom (2005), this is probably the best way of estimating

production functions when input prices are common across firms, and as a consequence they

cannot be used as instruments for input choices (in such a setting, it is probably preferable

to Olley and Pakes (1996) and similar methods). Alternatively, there could exist differences

12

in input prices across firms such as, for example, training subsidies which apply to firm

A but not firm B in an exogenous way, but these are unobserved in our data. Bond and

Soderbom (2005) show that in a model with adjustment costs for each input, past input

choices predict current input choices. Furthermore, since past input choices are made before

current productivity shocks are observed they are valid instruments for current input choices.

Given the evidence in Blundell and Bond (2000), we assume that the productivity shocks

in equation (3.2) follow an AR(1) process:

εjt = ρεjt−1 + ϕjt (3.3)

where ϕjt is for now assumed to be an i.i.d. process and 0 < ρ < 1. Taking logs from

equation (3.2) and substituting yields the following common factor representation:

lnYjt = lnAt + α lnKjt + β lnLjt + γhjt + θZjt + µj + ϕjt (3.4)

+ρ lnYjt−1 − ρ lnAt−1 − ρα lnKjt−1 − ρβ lnLjt−1 − ργhjt−1 − ρθZjt−1 − ρµj .

Grouping common terms we obtain the reduced form version of the model above.

lnYjt = π0 + π1 lnKjt + π2 lnLjt + π3hjt + π4Zjt + (3.5)

+π5 lnYjt−1 + π6 lnKjt−1 + π7 lnLjt−1 + π8hjt−1 + π9Zjt−1 + υj + ϕjt.

subject to the common factor restrictions (e.g., π6 = −π5π1,π7 = −π5π2), where υj =

(1− ρ)µj .

13

We start by estimating the unrestricted model in equation (3.4) and then impose (and

test) the common factor restrictions using a minimum distance estimator (Chamberlain,

1984). Empirically, we measure Yjt with the firm’s value added, Kjt with book value of

capital and Ljt with the total number of employees. Zjt includes time varying firm and

workforce characteristics - the proportion of males in the workforce, a cubic polynomial in

the average age of the workforce, occupational distribution of the workforce and the average

education of the workforce (measured by the proportion workers with high education) -

as well as time, region and sector effects. hjt will be computed for each firm-year using

information on the training history of each firm and making assumptions on the average

knowledge depreciation.

Since the model is estimated in first differences the assumption we need isE ϕjt − ϕjt−1 Xjt−2 =

0, where X is any of the inputs we consider in our production function. This is satisfied if

ϕjt (but not εjt) is essentally uncorrelated. Therefore, we allow the choice of inputs at t, Xjt,

to be correlated with current productivity shocts εjt, and even with the future productivity

shock εjt+1, as long it is uncorrelated with the innovation in the auto-regressive process in

t+1, i.e. ϕjt+1. In this case, inputs dated t−2 or earlier can be used to as instruments for the

first difference equation in t (similary, Yjt−1 can be instrumented with Yjt−3 or earlier). Blun-

dell and Bond (1998) point out that it is possible that these instruments are weak, and it may

be useful to supplement this set of moment conditions with additional ones provided that

E (Xjt−1 −Xjt−2) υj + ϕjt = 0, which is satisfied if E [(Xjt−1 −Xjt−2) υj ] = 0. These

assumptions are not unreasonable, since υj is fixed over time and in principle should not be

systematically correlated with the growth of inputs. The implication of these assumptions

is that we can use lags of the first differences of the endogenous variables as instruments for

14

the levels equation. In this paper we use both sets of moment conditions. We report the

Sargan-Hansen test of overidentifying restrictions.

In general, given the instrumental variables estimates of the coefficients, it is possible to

test whether the first difference of the errors are serially correlated. Unfortunately, given

the short length of the panel, we can only test for first order serial correlation of the resid-

uals, which we reject almost by construction (since a series of first differences is very likely

to exhibit first order serial correlation). The hypothesis that there exists higher order se-

rial correlation (which would probably invalidate our procedure) is untestable in our data.

Hopefully this is not a big concern. In the only other paper we know that applies these

methods for studying the impact of training on productivity (with data for the UK aggre-

gated by industry), Dearden, Reed and Van Reenen (2005) cannot reject that second order

serial correlation in the first differences of productivity shocks is equal to zero. In their orig-

inal application, Blundell and Bond (2000) also do not find evidence of second order serial

correlation using firm level data for the UK.

We assume that average human capital in the firm depreciates for two reasons. On the

one hand, skills acquired in the past become less valuable as knowledge becomes obsolete

and workers forget past learning (e.g, Lillard and Tan, 1986). This type of knowledge

depreciation affects the human capital of all the workforce in the firm. We assume that one

unit of knowledge at the beginning of the period depreciates at rate δ per period. On the

other hand, average human capital in the firm depreciates because each period new workers

enter the firm without training while workers leave the firm, taking with them firm specific

knowledge (e.g., Dearden, Reed and Van Reenen, 2005). Using the permanent inventory

formula for the accumulation of human capital yields the following law of motion for human

15

capital (abstracting from j):

Hjt+1 = ((1− δ)hjt + ijt)(Ljt −Ejt) +Xjtijt

where Hjt is total human capital in the firm in period t (Hjt = Ljthjt), Xjt is the number

of new workers in period t, Ejt is the number of workers leaving the firm in period t and it

is the amount of training per employee in period t.14 At the end of period t, the stock of

human capital in the firm is given by the human capital of those Ljt−Ejt workers that were

in the firm in the beginning of the period t (these workers have a stock of human capital

and receive some training on top of that) plus the training of the Xjt new workers. This

specification implies that the stock of human capital per employee is given by:

hjt+1 = (1− δ)hjtφjt + ijt (3.6)

where φjt =Ljt−EjtLjt+1

and 0 ≤ φjt ≤ 1. Our estimation procedure is robust to endogenous

turnover rates since they can be subsumed as another dimension of the endogeneity of input

choice.

Under these assumptions, skill depreciation in the model is given by (1−δ)φjt. We assume

that δ = 17% per period (although we will examine the robustness of our findings to this

assumption).15 We estimate the turnover rate from the data since we have information on

14We assume that all entries and exits occur at the beggining of the period. We also ignore the fact thatworkers who leave may be of different vintage than those who stay. Instead we assume that they are arandom sample of the existing workers in the firm (who on average have ht units of human capital).15Our choice of 17% is based on Lillard and Tan (1986), who estimate an average depreciation in the firm

is between 15% and 20% per year. Alternatively, we could have estimated δ from the data. Our attemptsto do so yielded very imprecise estimates.

16

the initial and end of the period workforce as well as on the number of workers who leave the

firm (average turnover in the sample is 14%). The average skill depreciation in our sample

is 25% per period. We measure ijt with the average hours of training per employee in the

firm.16 Since we cannot observe the initial stock of human capital in the firm (h0), we face

a problem of initial conditions. Under some restrictions the effect of h0 on firm productivity

can be subsumed in the firm fixed effect of equation (3.5).17 In spite of the problem of initial

conditions, we believe this approach is an improvement over the common practice of just

using the flow of training as an input, which implicitly assumes that the depreciation rate is

100%.

The semi-log linear production function we assume implies that human capital is com-

plementary with other inputs in production (∂2 lnY∂H∂X

> 0, where X is any of the other inputs).

However, we do not believe this is a restrictive assumption. In fact, it is quite intuitive that

16In approximately 3% of the firm-year observations we had missing information on training although wecould observe it in the period before and after. To avoid losing this information, we assumed the average ofthe lead and lagged training values. This assumption is likely to have minor implications in the constructionof the human capital variables because there were few of these cases.17More precisely, we can write:

hjt = (1− δ)tφj1...φjt−1hj0 +t−1

s=1(1− δ)s−1φjt−s...φjt−1ijt−s

where hj0 is the firm’s human capital the first period the firm is observed in the sample (unobservable inour data). Plugging this expression into the production function gives:

lnYjt = lnAt + α lnKjt + β lnLjt + γt−1

s=1(1− δ)s−1φjt−s...φjt−1ijt−s + θZjt + µjt + εjt

where µjt = γ(1− δ)tφj1...φjt−1hj0. However, µjt becomes a firm fixed effect if skills fully depreciate (δ = 1

or φjt = 0 for all t) or if there is no depreciation (δ = 0) and turnover is constant (φjt = φj). If 0 < δ < 1 and0 < φjt < 1, then µjt depreciates every period at rate (1− δ)φjt. If hj0 is correlated with the future sequenceof ijt+s then the production function estimates will be biased, and our instrumental variable strategy willnot address this problem. However, it is possible to estimate h0 by including in the production function afirm specific dummy variable whose coefficient decreases over time at a fixed and known rate (1− δ)φt. Thisprocedure is quite demanding in terms of computation and data, and in the present version of the paper weassume we can be reasonably approximate the terms involving h0 with a firm fixed effect.

17

such complementarity exists since labor productivity and capital productivity are likely to

be increasing functions of H (workers with higher levels of training make better use of their

time, and make better use of the physical capital in the firm). The only concern would be

that H and workers’ schooling could be substitutes, not complements (workers’ schooling is

one the inputs in Z). In this regard, most of the literature shows that workers with higher

levels of education are more likely to engage in training activities than workers with low

levels of education, indicating that, if anything, training and schooling are complements.

We are interested in computing the internal rate of return of an additional hour of training

per employee in the firm. From the estimates of the production function we can directly

compute the current marginal product of training (MBt+1). We assume that future marginal

product of current training (MBt+s,s=1 ) is equal to current marginal product of training

minus human capital depreciation (coeteris paribus analysis: what would happens to future

output keeping everything else constant, including the temporary productivity shock). To

obtain an estimate for the MFPjt, we must compute the marginal product of one hour of

work for each employee. Since our measure of labor input is the number of employees in the

firm, we approximate the marginal product of an additional hour of work for all employees by

MPLjt(Hours per Employeejt)

Ljt (whereMPLjt is the marginal product of an additional worker in firm

j and period t).18 Finally, since part of the training occurs outside the normal working hours

and our data set includes information on this share for each firm, we need to transform the

marginal product of one hour of work into the marginal foregone cost of one hour of training.

In our data, only 52% (on average) of the training hours takes place during normal working

18Alternatively, we could have included per capita hours of work directly in the production function.Because there is little variation in this variable across firms and across time, our estimates were very imprecise.

18

hours. To estimate marginal foregone productivity we multiply the marginal product of

labor by this proportion for each firm.

Given the concerns with functional form in the related wage literature, emphasized by

Frazer and Lowenstein (2005), we estimated other specifications where we include polyno-

mials in human capital in the production function. Since higher order terms were generally

not significant we decided to focus our attention on our current specification.

3.2. The Costs of Training for the Firm

In the previous section we described how to obtain estimates of the marginal product of

labor and, therefore, of the foregone productivity cost of training. Here we focus on the

direct costs of training. To estimateMCt, we need data on the direct cost of training. These

include labor payments to teachers or training institutions, training equipment such as books

or movies, and costs related to the depreciation of training equipment (including buildings

and machinery). Such information is rarely available in firm level data sets. Our data is

unusually rich for this exercise since it contains information on the duration of training,

direct costs of training and training subsidies.

Different firms face the same cost up to a level shift. We do not expect to see many

differences in the marginal cost function across firms since training is probably acquired in

the market (even if it is provided by the firm, it could be acquired in the market). Therefore

we model the direct cost function using levels of cost instead of log cost with a quadratic spline

in the total hours of training provided by the firm to all employees, with three knots (using

logs instead of levels gives us slightly lower marginal cost estimates). The knots correspond

to the 90th, 95th and 99th percentiles of the distribution of training hours. Our objective

19

is to have a more flexible form at the extreme of the function where there is less data, to

avoid the whole function from being driven by extreme observations. This specification also

makes it easier to capture potential fixed costs of training, that can vary across firms. In

particular, we consider:

Cjt = θ0+θ1Ijt+θ2I2jt+θ3D1jt(Ijt−k1)2+θ4D2jt(Ijt−k2)2+θ5D3jt(Ijt−k3)2+ σsDs+ηj+ξjt

(3.7)

where Cjt is the direct cost of training, Ijt is the total hours of training, Dzt is a dummy

variable that assumes the value one when Ijt > kz (z = 1, 2, 3), k1 = 15, 945, k2 = 32, 854,

k3 = 125, 251, Ds are year dummies, ηj is a firm fixed effect and ξj is a time varying cost

shock. We estimate the model using the Blundell and Bond (1998, 2000) system GMM

estimator (first differencing eliminates ηj and instrumenting accounts for possible further

endogeneity of Ijt). We described this method in detail already, and again we believe that

the identifying assumptions are likely to be satisfied by the cost function. In particular,

we assume that E (Ijt−1 − Ijt−2) ηj + ξjt = 0 and E ξjt − ξjt−1 Ijt−k = 0, k ≥ 2.

Empirically, Cjt is the direct cost supported by the firm (it differs from the total direct cost

of training by the training subsidies), and Ijt is the total hours of training provided by the

firm in period t.

One last aspect with respect to the cost function concerns the choice of not modelling

the temporary cost shock as an autoregressive process, as it was done for the production

function. In fact, we started with such a specifiction. However, when we estimated the

20

model the autoregressive coefficient was not statistically different from zero, and therefore

we chose a simpler specification for the error term.

From the above estimates we obtain ∂Cjt∂Ijt. To obtain the marginal direct costs of an

additional hour of training for all employees in the firm we compute ∂Cjt∂IjtLjt.

4. Empirical Results

Table 2 presents the estimated coefficients on labor and on the stock of training for alterna-

tive estimates of the production function.19 Column (1) reports the ordinary least squares

estimates of the log-linear version of equation (3.2), column (2) reports the first differences

estimates of the log-linear version of equation (3.2) and column (3) reports the system-GMM

estimates of equation (3.5). For the latter specification we report the coefficients after im-

posing the common factor restrictions. We also present the p-values for two tests for the

latter specification: one is a test of the validity of the common factor restrictions, the other

is an overidentification (Hansen-Sargan) test. We can neither reject the overidentification

restrictions nor the common factor restrictions.20 Our preferred estimates are in column (3)

because they account for firm fixed effects and endogenous input choice.

Columns (1) and (2) are presented for comparison. In particular, column (2) corresponds

to the most commonly estimated model in this literature (using either wages or output as the

dependent variable). The instrumental variables estimate of the effect of training on value

added in column (3) is well below the estimate in column (2). This may happen because

19The estimated coefficients for full set of variables included in the regression are presented in table A1 inthe annex.20We estimate the model using the xtabond2 command for STATA, developed by Roodman (2005).

21

firms train more in response to higher productivity shocks, generating a positive correlation

between temporary productivity shocks and investments in training. Curiously, Dearden,

Reed and Van Reenen (2005) also find that the first difference estimate overestimates the

effect of training on productivity, although the difference between first difference and GMM

estimates in their paper is smaller than in ours.

The estimated benefits in all the columns of table 2 seem to be quite high, even the GMM

estimate: a increase in the amount of training per employee of 10 hours (approximately

0.5% of the total amount of hours worked in a year21) leads to an increase in current value-

added which is between 0.6% and 1.3% (still, as far as they can be compared, we believe

this estimate is, if anything,smaller than other estimates of the benefits of training in the

literature). If the marginal product of labor were constant (linear technology), an increase in

the amount of training per employee by 10 hours would translate into foregone productivity

costs of at most 0.5% of output (if all training occurred during working hours). With

decreasing marginal product of labor (and because roughly 50% of training occurs outside

normal working time) foregone productivity is much lower. Given that the impact of training

on productivity lasts for more than just one period, ignoring direct costs would lead us to

implausibly large estimates of the return to training. As explained in the previous section,

we will use the coefficient on labor input in column (3) of table 2 to quantify the importance

of foregone productivity costs of training for each firm.

The results of estimating the direct training cost function in equation (3.7) are reported

in table 3. Again, for comparison, we report the estimates for different methods. Col-

21For an individual working 2000 hours a year, 10 hours corresponds to 0.5% of annual working hours.

22

umn (1) estimates the equation in levels with ordinary least squares, column (2) estimates

the equation in first differences with least squares and column (3) estimates equation with

system-GMM. The latter are again our preferred estimates since they account for firm fixed

effects and for the correlation between training and transitory cost shocks. We test and re-

ject that all coefficients on training are (jointly) equal to zero. We also test whether second

order correlation in the first differenced errors is zero and do not reject the null hypothesis.

Unfortunately we reject the standard test of overidentifying restrictions for the cost function.

Experimenting with different lagged instruments did not solve this problem.

The rejection of the test does not indicate necessarily that the set of instruments is

invalid. If the coefficients of the cost function vary across firms then we do not expect all

the instruments to estimate the same parameter. In fact, we expect exactly the opposite

(see Heckman and Vytlacil, 2005). Therefore, unfortunately we cannot distinguish whether

the overidentification test is rejected because there are some instruments which are invalid

or because there is heterogeneity in marginal costs.

We proceed to compute the marginal benefits and marginal costs of training for each firm.

On average, we estimate that foregone productivity accounts for less than 25% of the total

costs of training. This finding is of great interest for two related reasons. First, it shows that

a simple returns to schooling intuition is inadequate for studying the returns to training. In

particular, it is unlikely that we can just read the return to training from the coefficient on

training in a production function.22 The reason is that, unlike the case of schooling, direct

costs cannot considered to be negligible. Second, without data on direct costs estimates of

22As emphasized in Mincer (1989), this is likely to also be a problem in wage regressions.

23

the return to investments in training are of limited use given that direct costs account for the

majority of training costs. Unfortunately it is impossible to assess the extent to which this

result is generalizable to other datasets (in other countries) because similar data is rarely

available. However, given the absurd rates of return implicit in most of the literature when

one ignores direct costs (e.g., Frazer and Lowenstein, 2005), we conjecture that a similar

conclusion most hold for other countries as well.

Finally, table 4 presents the estimates of the internal rate of return (IRR) of an extra

hour of training per employee for an average firm in our sample, the average return for firms

providing training and the average return for firms not providing training.23 The results of

tables 2 and 3 assume a rate of human capital depreciation (δ) of 17%. In columns (1)-

(5) we display the sensitivity of our IRR estimates to different assumptions about the rate

of human capital depreciation (the production function estimates underlying this table are

reported in table A2). In our base specification, where we assume a 17% depreciation rate,

the average marginal internal rate of return is 9% for the whole sample. The average return

is negative (-7%) for firms not providing training and quite high (24%) for the set of firms

offering training. As expected, the higher the depreciation rate the lower is the estimated

IRR. In particular, under the standard assumption that δ = 100% (so that the relevant

input in the production function is the training flow, not its stock), the average IRR for the

marginal unit of training is negative when we take the sample as a whole. Notice, however,

that across columns the estimates in the second line of the table are always smaller or equal

than zero, and those in the third line of the paper are always positive. For reasonable rates

23In this paper heterogeneity in returns across firms does not come from a random coefficients specification,but from non-linearity in training and labor input in the production and cost functions.

24

of depreciation (which in our view are the ones in the first three columns of the table) returns

to training are quite high for the sample as a whole, and especially for the set of firms that

decide to engage in training activities.

We conjecture that the firms in the second line of the table do not offer training precisely

because they face low returns and therefore they may be acting rationally and optimally.

However, the returns for firms providing training are quite high, our lower bound being

of 17% and our preferred estimate being 24% (ignoring the estimates where we assume a

100% depreciation rate). With such high returns, it is puzzling why firms train such a small

proportion of the total hours of work (less than 1%24). One hypothesis is that suboptimal

amounts of training may be the result of a coordination problem, as emphasized in Pischke

(2005). Given that the benefits of training need to be shared between firms and workers,

each party individually only sees part of the total benefit of training. Unless investment

decisions are coordinated and decided jointly, inefficient levels of investment may arise. It is

also possible that firms would like to invest more in their workers but they are unable to do so

because they are constrained (e.g., credit constrained). In that case, investments in training

are likely to be suboptimal. Unfortunately we cannot verify empirically the importance of

these different hypotheses

Information problems and uncertainty in this investment in human capital could also lead

firms to invest small amounts in training even though the ex post average return is high (al-

though what really matters for determining the risk premium is not uncertainty per se, but

its correlation with the rest of the market). We find an enormous dispersion in the ex post

24From table 1 we can see that, in firms providing high amounts of training, hours trained per employeeper year are on average 19, while hours worked per employee per year are above 1800.

25

returns to training which may be suggestive of the importance of uncertainty. For example,

in our base specification the 5th percentile of the distribution of internal rates of return is

-16% and the 95% percentile is 66%. Under our current set up we cannot distinguish how

much of the variability in returns across firms is due to heterogeneity and how much is due

to uncertainty (as in, for example, Carneiro, Hansen and Heckman, 2003). However, here

uncertainty only comes from future productivity shocks (which interact with training in the

production function), since current cost and productivity shocks are assumed to be known

at the time of the training decision. We computed the R-Squared of our production func-

tions (after accounting for firm fixed effects). Our estimate (85%) suggests that temporary

productivity shocks can only explain 15% of the variation in output. Furthermore, since

productivity shocks are correlated over time this 15% is an overestimate of the amount of

uncertainty firms face. Therefore, it is unlikely the amount of uncertainty that is left can

justify such a high rate of return on human capital investments.

5. Conclusion

In this paper we estimate the internal rate of return of firm investments in human capital. We

use a census of large manufacturing firms in Portugal between 1995 and 1999 with unusually

detailed information on investments in training, its costs, and several firm characteristics.

Our parameter of interest is the return to training for employers and employees as a whole,

irrespective of how these returns are shared between these two parties.

We document the empirical importance of adequately accounting for the costs of train-

ing when computing the return to firm investments in human capital. In particular, unlike

26

schooling, direct costs of training account for about 75% of the total costs of training (fore-

gone productivity only accounts for 25%). Therefore, it is not possible to read the return

to firm investments in human capital from the coefficient on training in a regression of pro-

ductivity on training. Data on direct costs is essential for computing meaningful estimates

of the internal rate of return to these investments.

our estimates of the internal rate of return to training vary across firms. While in-

vestments in human capital have on average negative returns for those firms which do not

provide training, we estimate that the returns for firms providing training are quite high, our

lower bound being of 17% and our preferred estimate being 24%. Such high returns suggest

that company job training is a sound investment for firms and for the economy as a whole,

possibly yielding higher returns than either investments in physical capital or investments

in schooling. Therefore, it is puzzling why these firms train on average such a small pro-

portion of the total hours of work (less than 1%). We suggest three possible explanations:

1) coordination failures between employers and employees; 2) uncertainty in the returns to

training; 3) credit constraints. Unfortunately we cannot assess the empirical importance (if

any) of each of these hypotheses, although there is suggestive evidence that the uncertainty

hypothesis is relatively unimportant.

6. Data Annex

The data used is the census of large firms conducted by the Portuguese Ministry of Employ-

ment in the period 1995-1998. We restrict the analysis to manufacturing firms. All the firms

are uniquely identified with a code that allows us to trace them over time. This data collects

27

information on balance sheet information, employment structure and training practices. All

the nominal variables in the paper were converted to euros at 1995 prices using the general

price index and the exchange rate published by the National Statistics Institute.

In the empirical work, we use information for each firm on total value added, book value

of capital depreciation, total hours of work, total number of employees, total number of

employees hired during the year, total number of employees that left the firm during the

year (including quits, dismissals and deaths), average age of the workforce, total number of

males in the workforce, total number of employees with bachelor or college degrees, total

number of training hours (in internal and external training programs), total costs of training,

total training hours taking place outside the working period, firm’s regional location and firm

5-digit ISIC sector code.

We define value added per employee as total value added in the firm divided by total

number of employees, employees is the total number of employees at the end of the period,

Hours work per employee is the total hours of work in the firm (either working or training)

divided by number of employees, Capital depreciation per employee is the book value of

capital depreciation divided by number employees25, Labor costs per employee is the total

cost of labor for the firm (including wages, premiums, subsidies) divided by the total number

of employees, Share of high educated workers is the share of workers with more than secondary

education in the firm, Age of the workforce is the average age of all the employees in the

firm, Share males in the workforce in the share of males in the total number of employees

in the firm, Training hours per employee is the total number of hours of training provided

25We assume that depreciation is a linear function of the book value of the firm’s capital stock : Dept =π ∗Kt.

28

by the firm (internal or external) divided by the total number of employees, Training hours

per working hour is the total number of training hours provided by the firm (internal or

external) divided by the total hours of work in the firm, Direct cost per employee is the total

training cost supported by the firm (include, among others, the wages paid to the trainees or

training institutes and the training equipment, including books and machinery) divided by

the total number of employees, Average worker turnover is the total number of workers that

enter and leave the firm divided by the average number of workers in the firm during the

year, Average number of workers in the firm during the year is the total number of workers

in the beginning of the period plus the total number of workers at the end of the period

divided by two.

29

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32

No Training Firms Low Training Firms High Training FirmsValue added / Employees 2,228 3,471 5,230Employees 157 203 242Hours work / Employees 2,043 2,047 2,054Book Value Capital Depreciation 49,607 130,995 266,727Share high educated workers 0.013 0.031 0.061Average age workforce 37.3 39.3 40.7Share males workforce 0.42 0.61 0.71Occupations:

Share top managers 0.01 0.02 0.03Share managers 0.02 0.02 0.04

Share intermediary workers 0.04 0.05 0.05Share qualified workers 0.41 0.42 0.43

Share semi-qualified workers 0.21 0.21 0.21Share non-qualified workers 0.04 0.05 0.03

Share apprenteces 0.03 0.01 0.002Training hours / Employees - 1.6 18.9Training hours / Hours work - 0.001 0.009Direct Cost / Employee - 1.89 18.28Direct Cost / Value Added - 0.001 0.003Nb observations 2,586 1,458 1,467Source: Balanço Social

Table 1: Medians of Main Variables by Training Intensity

Nominal variables in Euros (1995 values). "Low training firms" are firms with less than the median hours of training per employee

(6.4 hours a year) and "High training firms" are firms with at least the median hours of training per employee. Employees is the total

number of employees in the firm. Total Hours/Employees is annual hours of work per employee, Capital's Depreciation is the

capital's book value of depreciation, "Share low educated workers" is the share of workers with at most primary education, Average

age is the average age of the workforce (years), Share males is the share of males in the workforce, Training hours/Employee is the

annual training hours per employee in the firm, Training hours / Hours work is the share training hours in total hours at work, Direct

Cost/Employee is the cost of training per employee and Direct Cost / Value Added is the cost of training as a share of value added.

All the variables defined in the annex.

Dependent variable: Log Real Value

Added per Employee

Log Real Value Added per Employee

Log Real Value Added per Employee

Method: OLS- Levels OLS-First Differences SYS-GMM(1) (2) (3)

Training Stock 0.0006 0.0013 0.0006(0.0002)*** (0.0002)*** (0.0003)*

Log Employees 0.79 0.56 0.77(0.01)*** (0.057)*** (0.11)***

Observations 4,327 2,816 2,816

P-Value Over-Identification Test - - 0.26P-Value Common Factor Restrictions - - 0.52

Table 2: Production Function Estimates

The table presents estimates of the production function assuming that (time invariant) human capital depreciation in the firm is 17%.

Column (1) presents the estimates with ordinary least squares, column (2) with first differences and column (3) with SYS-GMM.

Standard errors in parenthesis, *** Significant at 1%, ** Significant at 5%, * Significant at 10%. All specifications include the

following variables (point estimates not reported): log capital stock, share occupation group, share low educated workers, share

males workforce, cubic polinomial in average age workforce, year dummies, region dummies and 2-digit sector dummies.

Dependent variable: Real Training Cost Real Training Cost Real Training Cost

Method: OLS- Levels OLS-First Differences SYS-GMM(1) (2) (3)

Training Hours/1000 2046.3 901.6 7107.3(227.0)*** (331.1)*** (4693.7)

(Training Hours/1000)^2 -57.8 -19.1 -223.2(12.9)*** (16.7)*** (248.8425)

D1*(Training Hours/1000 -16)^2 115.3 39.8 187.1(20.5)*** (25.1) (339.0)

D2*(Training Hours/1000 -33)^2 -68.9 -27.4 53.0(8.7)*** (9.8)*** (99.4)

D3*(Training Hours/1000 -125)^2 11.6 7.1 -21.9(.61)*** (0.68)*** (8.9)**

Observations 5,511 3,908 5,511

P-Value F-test all slopes=0 0.00 0.00 0.00

Table 3: Estimates of the Cost Function

The table presents the estimates of the cost function. Column (1) presents the estimates with ordinary least squares, column (2) with

first differences and column (3) with SYS-GMM. Standard errors in parenthesis, *** Significant at 1%, ** Significant at 5%, *

Significant at 10%. D1 is a dummy variable equal to 1 when total annual training hours in the firm is higher than 15,000, D2 is a

dummy variable equal to 1 when total annual training hours in the firm is higher than 33,000 and D3 is a dummy variable equal to

1 when total annual training hours in the firm is higher than 125,000.

Depreciation Rate: 5% 10% 17% 25% 100%(1) (2) (3) (4) (5)

All Firms in Sample 14% 10% 9% 1% -28%

Firms not providing training 0% -4% -7% -14% -64%

Firms providing training 27% 22% 24% 17% 4%

Table 4: Marginal Return of a Training Hour for All Employees

Table reports the average marginal internal rate of return for different assumptions on the (time invariant)

human capital depreciation in the firm. Marginal benefis and marginal costs were obtained with the SYS-

GMM estimates in columns (3) of table 2 and column (3) of table 4, respectively.

Dependent variable:

Log Real Value

Added per Employee

Log Real Value

Added per Employee

Log Real Value

Added per Employee

Log Real Value

Added per Employee

Log Real Value

Added per Employee

Depreciation Rate: 5% 10% 17% 25% 100%(1) (2) (3) (4) (5)

Training Stock 0.0005 0.0005 0.0006 0.0006 0.0013(0.0003)* (0.0003)* (0.0003)* (0.0003)* (0.0008)

Log Employees 0.75 0.76 0.77 0.78 0.85(0.11)*** (0.11)*** (0.11)*** (0.12)*** (0.14)***

Observations 2,816 2,816 2,816 2,816 2,816

P-Value Over-Identification Test 0.26 0.26 0.26 0.26 0.33P-Value Common Factor Restrictions 0.54 0.51 0.52 0.54 0.42

Table A1: Production Function Estimates: Sensitivity to Different Depreciation Rates

The table presents the SYS-GMM estimates of equation (3.4) in the text for different assumptions on the (time invariant) human capital

depreciation in the firm. Standard errors in parenthesis, *** Significant at 1%, ** Significant at 5%, * Significant at 10%. All

specifications include the following variables (point estimates not reported): capital stock, share occupation group, share low educated

workers, share males workforce, cubic polinomial in average age, year dummies, region dummies and 2-digit sector dummies.

Dependent variable: Log Real Value Added per

Employee

Log Real Value Added per Employee

Method: SYS-GMM SYS-GMM

Unrestricted Common Factors

Restricted Common Factors

Value Added per Employee t-1 0.243 -[0.113]**

Training Stock t 0.001 0.0006[0.001] [0.0003]*

Training Stock t-1 -0.001 -[0.001]

Log Employees t 0.734 0.7718[0.241]*** [0.117]***

Log Employees t-1 -0.149 -[0.242]

Log Capital Stock t 0.132 0.2476[0.120] [0.045]***

Log Capital Stock t-1 0.06 -[0.111]

Occupations: Share top managers t 5.0660 3.7722

[6.131] [3.102]*Share top managers t-1 -2.5100 -

[5.017]Share managers t 4.2640 4.9432

[6.654] [2.87]*Share managers t-1 -1.2060 -

[5.179]Share intermediary workers t 5.0550 5.9298

[7.091] [3.110]*Share intermediary workers t-1 -1.0770 -

[5.411]Share qualified workers t 4.5500 5.0089

[6.612] [2.877]*Share qualified workers t-1 -1.2810 -

[5.227]Share semi-qualified workers t 4.2190 4.828

[6.666] [2.881]*Share semi-qualified workers t-1 -1.1040 -

[5.272]Share non-qualified workers t 3.8750 4.8915

[6.365] [2.879]*Share non-qualified workers t-1 -0.9260 -

[5.079]Share apprenteces t 3.2520 4.8873

[6.329] [2.920]*Share apprenteces t-1 -0.1990 -

[4.986]Share High Educated workers t 1.4930 2.3461

[1.161] [0.561]***Share High Educated workers t-1 0.1220 -

[0.414]Share males workforce t -1.09 0.8308

[1.375] [0.331]***Share males workforce t-1 1.772 -

[1.320]

Observations 2,816 2,816

Autocorrelation Coefficient - 0.1256[0.057]***

Columns (1) and (2) present the estimates of equation (3.3) and (3.4) in the text, respectively, with SYS-GMM,

assuming that (time invariant) human capital depreciation in the firm is 17%. Standard errors in parenthesis,

*** Significant at 1%, ** Significant at 5%, * Significant at 10%. The regressions also include year, region,

sector dummies and a cubic polinomial on average age workforce.

Table A2: Production Function Estimates